# Probability Theory - History Of Probability Theory, Counting, Experiments, Rules Of Probability, Empirical Probability, Using Probabilities

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chance events six mathematics

Probability theory is a branch of **mathematics** concerned with determining the long run **frequency** or chance that a given event will occur. This chance is determined by dividing the number of selected events by the number of total events possible. For example, each of the six faces of a die has one in six probability on a single toss. Inspired by problems encountered by seventeenth century gamblers, probability theory has developed into one of the most respected and useful branches of mathematics with applications in many different industries. Perhaps what makes probability theory most valuable is that it can be used to determine the expected outcome in any situation from the chances that a plane will crash to the probability that a person will win the lottery.

## Additional Topics

The branch of mathematics known as probability theory was inspired by gambling problems. The earliest work was performed by Girolamo Cardano (1501-1576) an Italian mathematician, physician, and gambler. In his manual Liber de Ludo Aleae, Cardano discusses many of the basic concepts of probability complete with a systematic analysis of gambling problems. Unfortunately, Cardano's work had lit…

A theoretical approach to determine probabilities requires the ability to count the number of ways certain events can occur. In some cases, counting is simple because there is only one way for an event to occur. For example, there is only one way in which a 4 will show up on a single roll of a die. In most cases, however, counting is not always an easy matter. Imagine trying to count the number of…

Probability theory is concerned with determining the likelihood that a certain event will occur during a given random experiment. In this sense, an experiment is any situation which involves observation or measurement. Random experiments are those which can have different outcomes regardless of the initial conditions and will be heretofore referred to simply as experiments. The results obtained fr…

By assuming that every outcome in a sample space is equally likely, the probability of event A is then equal to the number of ways the event can occur, m, divided by the total number of outcomes that can occur, n. Symbolically, we denote the probability of event A as P(A) = m/n. An example of this is illustrated by drawing from a deck of cards. To find the probability of an event such as getting a…

Probability theory was originally developed to help gamblers determine the best bet to make in a given situation. Suppose a gambler had a choice between two bets; she could either wager $4 on a coin toss in which she would make $8 if it came up heads or she could bet $4 on the roll of a die and make $8 if it lands on a 6. By using the idea of mathematical expectation she could determine which is t…

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## User Comments

about 8 years ago

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